1

## A study into identity formation:

## Troubling stories of adults taming

## mathematics

## Tracy Part

## A thesis submitted in partial fulfilment

## of the requirements of

## London Metropolitan University for

## the degree of Doctor in Philosophy

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### Table of

### Contents

Abstract ... 6 Acknowledgements ... 8 Glossary of terms ... 9 List of acronyms ... 10 List of tables ... 11 List of appendices ... 11 Introduction... 12 Thesis outline ... 12The aims of this research are: ... 15

Chapter 1: Introducing the field of study... 16

1.1 The Further Education sector ... 16

1.2 An historical overview of the sector ... 18

1.2.1 Volunteerism and philanthropy ... 18

1.2.2 Emergence of a national policy ... 19

1.2.3 A recent history of the FE sector ... 21

1.3 The mathematical spaces created by policy discourse ... 24

1.4 Summary ... 29

Chapter 2: The literature review... 30

2.1 Situating this PhD within the existing body of research ... 30

2.2 Constructivist conversations of power and social justice ... 31

2.3 A turn towards Lacan ... 32

2.4 Gendering mathematics ... 34

2.5 Critical rejection of the unitary individual... 36

2.5.1 Identity positioning and discursive construction ... 38

2.6 Summary ... 42

Chapter 3: The theoretical framework (introduction change) ... 44

3.1 Bourdieu's theory of practice... 45

3.1.1 Habitus ... 47

3.1.2 Capitals ... 48

3.1.3 Field ... 49

3.1.4 Bourdieu and discussions of power, hierarchies and social spaces ... 50

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3.2.1 Technologies of power ... 53

3.2.2 The subject, subjectification and subjectivities ... 54

3.2.3 Bourdieu, Foucault and visceral embodiment ... 56

3.4 Lacan’s psychoanalysis ... 58

3.4.1 The mirror stage ... 59

3.4.1 Fantasy, desire and loss ... 60

3.4.3 The imaginary, the symbolic and the real domains ... 60

3.4.4 Lacan and the illusion of choice ... 62

3.5 Summary: Rationale for looking to post-structuralism for this study ... 63

Chapter 4: Methodology ... 65

4.1 Situating the self as a researcher ... 66

4.2 Selection, recruitment and access to the learner participants ... 69

4.2.1 Recruitment ... 72

4.2.2 Access to participants... 73

4.3 Ethics and anonymity and collecting data ... 74

4.4 Justification of the data collection tools ... 77

4.4.1 Document analysis ... 78

4.4.2 Teachers group discussion ... 79

4.4.3 Life history interview ... 79

4.4.4 Non-participatory observations ... 81

4.4.5 Semi-structured interview ... 81

4.5 Analysing the data and organising the data ... 82

4.5.1 Critical discourse analysis in a Foucauldian tradition... 82

4.5.2 Storying the participant ... 83

4.6 Organising the data ... 85

4.7 Summary ... 86

Chapter 5: Historical locations ... 88

5.1.1 Numeracy linked to productivity ... 88

5.1.2 Markings of difference ... 89

5.1.3 Invited subjects ... 91

5.1.4 Contemporary configurations of the ‘dangerous classes’ ... 93

5.2 Structures of identification; subjects constructed by numeracy ... 96

5.2.1 *The 1959 Crowther Report* ... 96

5.2.2 *The 1982 Cockcroft Report* ... 99

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5.3 Structures of identification; teachers constructed by discourses ... 102

5.3.1 The production of the ‘ethical’ teacher ... 102

5.3.2. Skills for Life and the technologies of administration ... 104

5.4 Media discourses of numeracy, mathematics and mathematicians ... 107

5.4.1 Discourses of numerate employees and citizens ... 107

5.4.2 The crisis, ‘Get On’ and the gremlin within ... 108

5.4.3 The jettisoned abject ‘Other’ and an-other ... 109

5.4.4 Gendered discourses of ‘being’ mathematical ... 114

5.5 Summary ... 116

Chapter 6: ‘Private’ discourses of mathematics ... 118

6.1.1 Introduction to Steve: “Becoming academical” ... 119

6.1.2 Introduction to Jalal: “It doesn’t help me … destroy me little bit” ... 121

6.1.3 Introduction to Philly: “There’s a lot of people like me, out there” ... 122

6.1.4 Introduction to Fatima: “The silliness of education” ... 123

6.2 “Storying” Steve ... 125

6.3 “Storying” Jalal ... 131

6.4 “Storying” Philly ... 139

6.5 “Storying” Fatima ... 144

6.6 Summary ... 155

Chapter 7: Learners negotiating regulatory discourses ... 158

7.1 Learners ‘take on’ discourses of collaborative learning ... 159

7.2 Learners resisting ... 164

7.3 Learners negotiating ... 168

7.3.1 Silence and the classroom ... 174

7.4 Summary ... 179

Chapter 8: Teachers negotiating the demands of the reform agenda ... 181

8.1 Regulatory gaze... 181

8.2 Teachers negotiating best practice... 184

8.3 Teachers negotiating creativity and innovation ... 187

8.4 Connections between teacher and learner narratives ... 194

8.5 Summary ... 199

Chapter 9: Fragile Mathematics ... 202

9.1 Gendering of mathematics ... 203

9.2 Taming mathematics? ... 211

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9.3 Splitting mathematics ... 216

9.4 Summary ... 223

Chapter 10: Conclusions ... 227

10.1 Key findings and themes ... 228

10.1.1 Subjects positioned by discourse ... 228

10.1.2 Masculinities / femininities of mathematical knowledge ... 230

**10.1.2** Learners undergoing identity work ... 231

10.1.3 Splitting mathematics and the mathematical self ... 232

10.2 Discussions and implications ... 234

10.2.1 Methodology and theoretical framework ... 234

10.2.2 Implications: Noises of learning ... 235

10.2.3 Limitations of the study and the future ... 237

References... 239

Appendix 1: Visual representation of the national qualification framework ... 267

Appendix 2: Details of the sampling and selection processes for the document analysis ... 268

Appendix 3: Reflections on collecting data ... 271

Reflections on conducting the group discussion ... 271

Reflections on life history interviews ... 272

Appendix 4: Planning group discussion ... 274

Appendix 5: Interview topic guide ... 276

Appendix 6: Semi-structured interview questions ... 279

Appendix 7: Participant table ... 281

Appendix 8: Information sheets ... 284

Appendix 9: Consent forms ... 290

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**Abstract **

This thesis investigates how adult learners continuously negotiate their relationship with schoolroom mathematics through discourses akin to being ‘more’ or ‘less’ able to ‘do’ and ‘be’ mathematical. It argues that mathematical identities are politically and socially constructed, and that available forms of knowledge inscribe particular mathematical practices on the individual in the classroom. By paying attention to the precarious and contradictory productions of the self, and investigating the allure of undergoing a transformation of the self, I contribute to critical understandings of the psychic costs of re-engaging with learning mathematics as an adult learner.

This analysis is a critical narrative inquiry of stories of adults (not)taming

mathematics. As an iterative study into identity formation it puts theory to work in unusual ways. In bringing together internal and external processes (and the

intersection of biography, aspiration and discursive practice), I unmask how

participants underwent what Mendick (2005) calls “identity work”. Working with a Lacanian psychoanalytical through a Foucauldian tradition, I navigate the construction of selfhood during processes of reinvention as (non)mathematical subjects,

experiencing ‘success’(and alienation) through models of collaborative learning, in the contemporary mathematical classroom.

The study examines the lived experiences of 11 adult learners using a range of

qualitative methods. I actively seek the complexities within various types of provision (including adult education, further education, work-based learning, and community outreach programs) and the multiple forms of knowledge available (or not) through authoritarian discourses of education.

Engaging a mobile epistemology, this thesis connects subject positions, techniques of power, psychic costs of reinventing the self, and how the processes of visceral

embodiment of mathematics affects learning in the classroom. It argues that mathematical identities are discursively constructed, and the relationship between selfhood and ‘being’ and ‘doing’ mathematical-ness is told as much through narratives characterised by affection as by fear. Rather than provide answers or ‘best practice’

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for the collaborative classroom, I conclude with an explanation of why I question common sense assumptions, such as that adult learners want to be placed in a

hierarchical positions and judged as independent mathematical thinkers in class, and the practical implications for this in the classroom.

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**Acknowledgements **

I would first like to say a heart-felt thanks to the participants of the study. The

openness of their responses, critical reflections of their encounters of mathematics, the generosity of time, and the ways in which they made me feel welcome, have made this thesis possible.

My greatest thanks go to Jayne Osgood for encouraging and gently directing my intellectual journey. And to Alistair Ross, for stepping in during the write-up stage and helping me to translate my dense writing style into readable phrases, and for the valuable advice on joining together the critical policy perspectives. I would also like to thank Cathy Larne who has quietly and efficiently organised the administrative processes of this journey. Jayne, Alistair and Cathy have provided unfailing and patient support throughout this project, but I would also like to extend my thanks to Anthea Rose who was very briefly a supervisor, but who has frequently met me for lunch, discussed my ideas and encouraged me back to the library, to complete the day’s work.

I would also like to express a huge gratitude to the surgeons who organised the logistics of the operations around the completion of this thesis, and to the neurologist who provided valuable advice on how to organise my work schedule, and the

examination process. I would also like to thank the staff at London Bridge railway station, without whose support, comfort and training in meeting the needs of disabled passengers, I would never have had the confidence to use public transport and to attend the University and to complete the field work.

Finally, I would like to thank my friends and family; my mum and dad; sisters and Dan. And especially to Ruth, Maria and Julia, who patiently read through this thesis, and Helen and Rose, who listened whilst I was struggling to re-engage and gave me the confidence and encouragement to complete this journey.

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**Glossary of terms **

Adult Basic Skills Generic term used to describe basic mathematics and

English for adults.

Adult Numeracy Numeracy curriculum designed for adults mapped against primary and secondary schooling outcomes. Community learning Community learning includes a range of

community-based and outreach learning programmes. These are primarily funded by local authorities and further education colleges. They typically offer entry-level qualifications.

Discrete mathematics A mode of studying mathematics where mathematics is the only qualification output.

Embedded mathematics A mode of study where learning mathematics is one element of a wider, usually vocationally-based qualification.

Functional mathematics Functional mathematics is a set of standards with the criteria guided by standards for assessment.

Skills for Life The skills-set defined by the curricula for Adult Numeracy, Adult Literacy and English for Speakers of Other Languages.

Work-based Learning Work-based learning comes in many forms and includes internships, mentoring, and apprenticeships. The costs are typically met by the employer and the programme specific to the needs of the employment. The classes typically take place in the workplace.

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**List of acronyms**

AE Adult Education

ALLN Adult Literacy, Language and Numeracy CPD Continual Professional Development

DBIS Department for Business Innovation and Skills DfES Department for Education and Skills

DIUS Department for Innovation, Universities and Skills ESOL English as a Second or Other Language

FE College Further Education College

GCSE Examinations typically taken at the age of 16 IFL Institute for Learning (now defunct)

M4L Maths for Life

NCETM National Centre for Excellence in the Teaching of Mathematics NIACE National Institute of Adult Continuing Education

NRDC National Research and Development Centre QCA Qualifications and Curriculum Authority SFA Skills Funding Agency

SfL Skills for Life

TLRP Teaching and Learning Research Programme TTM Thinking Through Mathematics

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**List of tables **

Table 1: Timescale of study

Table 2: Details of the sample of participant teachers Table 3: Details of the sample of learner participant

Table 4: Schedule of data collection per provision November 2010 – June 2011 Table 5: Splitting maths into do-able and un-do-able forms of knowledge

**List of appendices **

One: Visual representation of the national qualification framework Two: Sampling process for document analysis

Three: Reflection on collecting data Four: Planning group discussion Five: Interview Topic guide Six: Semi-structured interview Seven: Participant table

Eight: Information sheets Nine: Consent forms

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**Introduction **

**Thesis outline **

This thesis is divided into ten chapters. The introduction sets out my positioning as an insider to the field, the aims of the research and a chapter-by-chapter outline of the thesis. Through setting a context of the field of study, Chapter One maps the policy context, discursive constructions of collaborative learning, and explains the

mathematical spaces on offer within the sector. Through a review of relevant literature, Chapter Two draws particular attention to the studies that have informed and shaped this research. Chapter Three engages with discussions of putting multiple theoretical perspectives to work, but also provides a critical account of Bourdieu (habitus, capitals and field), Foucault (technologies of power and subject positioning) and Lacan (the mirror stage, fantasy/desire and lacking, and the imaginary, symbolic and real domains) to map the analytical tools, which I have used to illustrate how mathematical relationships are fraught with emotion, tension, silences and antagonism.

Chapter Four is separated into six parts. In the first I situate myselfas a researcher. I pay attention to the ways in which my identity fragmented, as I removed the markers of professionalism that I was once privileged to as a teacher. Section two offers a largely descriptive account of the research design and process. In the meantime, parts three, four and five provide a reflective account of the ethical decisions that I wrestled with, and in-depth debate of the data collection and analytical methodological

considerations that have informed the findings of this study. Part six returns to a largely descriptive account of how I ‘tamed’ and organised the unruly life history interviews and lesson observations into manageable chunks for analysis through Chapters Six to Nine.

Chapter Five involves a critical deconstruction of government policy discourses to illuminate the history of the present construction of mathematics, numeracy (and the numerate citizen), and the production of ‘employable’ subjects. Through

problematising official policy texts, I expose the ways in which the adult ‘numeracy’ learner has been constructed, and to what effect. Chapters Six, Seven, Eight and Nine

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draw directly from the primary data gathered. Chapter Six ‘stories’ four ‘larger than life’ participants to establish (and maintain) a sense of the human that lies behind identity work. I put the theories to work, to deconstruct the conditions that have created the possibilities of truths about (not)learning, as understood by each of these four individuals. Having reached conclusions of the structural account, I then add to the discussion by interrogating the effects of positioning and identity work within the classroom.

Chapter Seven is concerned with the ways in which the learner participants wrestled with different social constructions of ‘being’ mathematical; notably through attention to the political and social locatedness of the subjectivities on offer to them as adult learners, particularly within discourses of collaborative learning. Chapter Eight takes the discursive construction of ‘best practice’, professionalism and standards as its focus. I look to the primary sample of teachers to explore their various productions of the self and of performative discourses of ‘best practice’. I achieve this by drawing upon the ways in which they reject, negotiate and reconcile ideal constructions of the ethical teacher through the (mis)alignment of historical and contemporary encounters of education and mathematics.

Chapter Nine considers the participants’ locations within, and their contributions to, a complex and contradictory discursive landscape of ‘being mathematical’. By attending to gendered, classed and raced constructions of mathematics I reveal, how on being confronted with ‘success’, the adult learner looks to stereotypes to reconcile their sense of selfhood as they undergo transformation into (non)mathematical subjects. In particular I unmasked how, through techniques of splitting mathematics into do-able and un-do-able forms, the participants recount stories of ‘taming’ the body of

knowledge and/or the gremlins lurking within. Finally, Chapter Ten offers a brief synthesis of the main thrust of my argument, an overview of the main findings and a consideration of the implications of this study for future research and professional practice.

14 Positioning myself as an insider to the field

Until 2010 I had, for fifteen years, been a teacher (and latterly a teacher trainer) of mathematics for adults returning to the classroom to learn numeracy. I have chosen to study the field of identity/discursive formation, because I realise that during this time I had almost exclusively focused my pedagogic gaze on ways to develop mathematical thinking. I had neglected the complexities of social positioning, and particularly the social construction of what it means to be mathematical. I had not recognised the importance of theorising the inherent instability and disunity within the site of the ‘self’, the effects of power and/or the compulsion to continuously undergo identity work; particularly as learners are confronted by new (and often unrecognisable) configurations of ‘success’ in the mathematical classroom.

During the six years that it has taken to complete this study there have been three different governments, each of which have reworked the ways in which the learning of mathematics is organised within the sector. In undertaking this thesis, I have

interrogated the peculiarities of the production of ‘doing’ mathematics, of ‘being’ numerate and of the ‘responsible’ citizen, in particular in relation to the policy

discourses that were pertinent at the time that the data was collected (December 2010 – April 2011). However, in revealing the history of the present, and the complexities behind the compulsion to undergo identity work, I have unmasked how the

subjectivities of the adult learner (once judged as not having the ability to ‘do’ mathematical thinking, now positioned as agentic ‘mathematical’ creators in the classroom) are inherent within, and through, the disruptions of the policy cycles and the changes to the curricula.

I achieve this by interrogating narratives of learner participants, as they recall stories of how they have come to ‘tame’ (or bypass) the unruly mathematics that they once encountered. In doing so, I reveal the ways in which these participants have

challenged, resisted, and/or taken up public discourses that construct the sector. I have taken particular interest in aspects of mathematical knowledge that have been

valorised and/or devalued, within and through these empirical collections of (not) learning mathematics.

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**The aims of this research are: **

to consider how public discourses position adult learners returning to the classroom, to learn numeracy, functional skills mathematics, and/or GCSE mathematics;

to examine the compulsion to undergo identity work as the learners negotiate their mathematical practices through the classed, gendered and 'raced'

trajectories of their identities;

to interrogate gendered narratives of the constructions of ‘doing’ mathematics and ‘being’ mathematical;

to unmask how learners use the technique of ‘splitting’ mathematics, as they draw on discourses to position themselves as more or less ‘able’ to do mathematics.

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**Chapter 1:**

**Introducing the field of study**

This chapter is formed of three parts. In section one I provide an overview of the sector, and in the second section I outline the historical, political and economic contexts for policy, with particular attention paid to the Skills for Life (SfL) Strategy that was pertinent at the time the data were collected. In section three I briefly

consider the discourses of ‘choice’ for adults returning to the sector to learn

mathematics, before outlining the pedagogic assumptions that have constructed spaces for learning mathematics.

**1.1 The Further Education sector **

Hillier (2015) describes Further Education (FE) as comprising the voluntary, public
and private sectors, funded through agencies, governments, employers and individuals
and catering for approximately six million students. The FE sector primarily offers
vocational training at foundation and intermediate1_{ levels, to learners over the age of }

16, although the provision caters for students from the age of 14 as an alternative to
the traditional models of schooling. The FE sector also caters for individuals who are
highly technically skilled, and who study academic courses at undergraduate and
postgraduate levels2_{. This, according to Crawley (2013), makes the FE sector one of }

the most complex and difficult areas of the educational landscape to define. Huddleston and Unwin (2013), offer a description of the FE sector as constructed from a richness, diversity, and range of qualifications that is unlike any other, producing a population heterogeneity that is simply different to schools and universities. Ursula Howard (2009), of the National Institute of Adult Continuing Education (NIACE), suggests that FE is most accurately reflected through an understanding of the diversity of the material, social, affective, and cognitive characteristics of those individuals returning to the classroom as adult learners. In

1_{ An intermediate qualification is considered to be equivalent to the threshold qualifications taken at the }
age of 16 by the majority of the population in England.

2 Refer to Appendix 1 for a visual explanation of the national qualification framework calibrated
against the qualifications offered through the compulsory and the Higher Education sectors*.*

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trying to frame this diversity, Howard (2009: 4) has compiled a “fact sheet”, to which I have added the final two points.

In 2006, 67% of those in receipt of Education Maintenance Allowances were studying in the sector.

In 1996, 80% of the adult learners studying within the sector were over 19 years old. By 2007, the figure had dropped to 62% of the learner population (NIACE, 2012).

In 2009:

90% of all adult language, literacy and numeracy (ALLN) courses that were offered in the UK were delivered within the sector.

The sector provided 48% of entrants to Higher Education.

59% of all HNDs and 86% of HNCs that were undertaken by learners in England were delivered in the sector.

Over 80% of all ESOL learners were studying English in the sector.

18% of learners were from ethnic minorities, compared to 11% of the general population.

However, with the increase in apprenticeships available to adults, the proportion by 2013 had increased to 76% of the student population (SFA, 2014).

In 2013, the Further Education sector catered for over 6 million students and employed over 1.3 million members of staff (Crawley, 2013).

By far the largest provision (and therefore the one that tends to dominate policy discussions) is the Further Education (FE) College (Foster, 2005), followed by Adult Education (AE) and the prisons system, although since 2006 there has been an

increasing number of private training institutes (NIACE, 2012). Training institutes fall within the sector, but tend to be privately owned and hold the specific instruction to meet the employment-based learning needs of young adults in transition from

compulsory schooling to employment (NIACE, 2012). Alongside, but funded through separate channels, are the smaller ‘non-formal’ community-based provisions that tend

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towards non-qualification learning outcomes. Such courses include family learning, community outreach, Trade Union, as well as other work-based learning programmes (Colley, Hodkinson & Malcolm, 2002). The implication of the experiences of learning mathematics through one form of provision, as opposed to another, is central to the discussion threads and the findings of this thesis.

**1.2 An historical overview of the sector **

**1.2.1 Volunteerism and philanthropy **

Adult Education as a concept emerged prior to the establishment of a state-funded educational system. Rooted primarily through the social critique that arose within and through the turmoil of the industrial revolution (Hillier, 2006), the primary providers were the Mechanics Institutes (MI) who drew from the Enlightenment philosophies to inform the shape of provision. In a bid to wrestle power away from religious

institutions, MIs looked to the rationality of the sciences to secularise education and to establish a body of “really useful knowledge” (Johnson, 1993: 17) to be learnt through “an atmosphere of open enquiry” (Benn, 1997: 67). But as can be seen from the quote below, in taking a classical liberal approach, the protagonists intended to separate adults perceived to be capable of engaging with esoteric forms of knowledge from the wider population, who were offered technical forms of instruction:

It is incumbent upon us to take care that our managers, our foremen, and our workmen, should, in the degree compatible with their circumstances, combine theoretical instruction with their acknowledged practical skill (Samuelson et al., 1884: 508).

Born of these classed trajectories, Working Men’s Associations (WMA) began to emerge offering an alternative curriculum comprised of “general literacy through cultural, and political education” (Hyland & Merrill, 2003: 6). Watson and Maddison (1908) suggests that the architects of the late nineteenth century adult education provision discursively constructed education as a liberatory tool for social change, and through a comparison of the quotes below, can be seen as remaining surprisingly similar to the contemporary (albeit diminishing) discourses of the community outreach settings.

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Thomas Burt, first Labour MP, 1870:

We say educate a man, not simply because he has got political power, and simply to make them a good workman; but educate him because he is a man (quoted in Watson & Maddison, 1908: 104).

University and College Union (UCU) Congress 2012:

Congress believes education is a right not a privilege, and all members of society should be able to access appropriate programmes (Congress, 2012: 6).

**1.2.2 Emergence of a national policy **

At the first Great Exhibition of 1851, held in London, British exhibits won most of the
prizes. But in 1867, when Napoleon hosted the second International Exposition in
Paris, the British exhibits failed to make an impression, and were simply reported in
the national press as a “poor showing” (Hillier, 2006: 21). In the political aftermath of
this embarrassment, the British government established a select committee and two
royal commissions to inquire into the state of technical instruction in the UK. As a
result, the City and Guilds of London Institute was formed in 1877, instructed to
devise accreditation for vocational training (Leathwood & Francis, 2006). The
*Technical Instruction Act 1889* brought, according to Hillier (2006), new powers for
boroughs to “devote a penny per person” (Hillier, 2006: 22), from rates raised from a
tax on alcohol spirits, “… to technical and manual instruction” (Hillier, 2006: 22).
Although adult educational opportunities tended to remain in the form of training, and
principally the responsibility of employers (Field, 1996), a range of technical colleges
began to emerge (Hurt, 1971).

Hillier (2006) cites this Act as an historic marker for the sector, because the particular nature of this funding stream (principally raised from taxes on the buying and selling of whisky) changed public discourses on the purpose of the sector. Where the

philanthropic and voluntaristic movements had once held discussions over the ethics
of poverty, the *Technical Instruction Act* justified political involvement in adult

education through discursively constructing the effects of the underperforming British
economy, paralysed by a skills shortage (Hyland and Merrill, 2003), and the “…
terrors of foreign competition” (Wolf, 2009: 58). Although the distaste for practical
instruction is not as apparent as in *The Taunton Report *(Schools Inquiry Commission,
1868/ London: HMSO), in relation to the teaching of mathematics, the shape - and the
subjectivities on offer - continue to be bound within this complex taxonomy, which in

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the contemporary setting still separates the academic adult from the technical adult,
who is separated again from the non-academic adult (Pring *et al*., 2012).

The* Education Act 1902* laid the foundations for a locally co-ordinated, national
system and provided the framework for policy construction until the *Education Act *
*1988 *(Hyland & Merrill, 2003). In what Ball (1990) refers to as the post-war

consensus, the *Education Act 1944* reasserted the responsibility of local authorities to
secure a provision with a focus on apprenticeships (Field, 1996). Benn (1997) and
Schuller and Watson (2009) each point to the establishment of Local Education
Authorities, and the normalisation of day-release learning programmes, as an

historical pointer for when the concept of ‘educational opportunities for all’ began to emerge as an imaginable ‘right’ within the psyche of the nation.

*The Crowther Report* (1959) brought about a new era for vocational training, citing
FE as the “next battleground for English education” (Crowther, 1959/ London:
HMSO: chapter 30). Crucial to this thesis, the concept of numeracy was discursively
constructed as a social and political means to address inequality, at the point at which
schoolboys made the transition between school and employment (Hillier, 2006).
However, whilst the *Industrial Training Act 1964* brought about a new political

ascendency for FE, the shape of mathematics education was primarily informed by the discursive link that justified the cost of FE through a promise of economic growth and social stability. The (lack of) impact of Crowther’s numeracy (as an alternative

curriculum space) will be explored in Chapter five, but the epistemological

consistencies between the mathematics on offer in the 1870s, and Crowther (1959) and the introduction of functional skills (QCA, 2007) are interesting to note, and can be seen from the following quotes:

*The Devonshire Report on the Advancement of Science, 1874: *

... but the true teaching of Science consists, not merely in parting facts … but in habituating the pupil to observe for himself, to reason for himself on what he observes, and to check the conclusions at which he arrives (Devonshire Association, 1874: 12).

*The Crowther Report into changing nature of social and industrial needs, 1959: *
On the one hand is an understanding of the scientific approach to the study of
phenomena – observation, hypothesis, experiment, verification. On the other

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hand is a need in the modern world to think quantitatively, to realise how far our problems are problems of degree, even when they appear as problems of kind (Crowther, 1959/ London: HMSO: para. 401).

Qualifications and Curriculum Authority (QCA) definition of functional skills, 2007:

Functional mathematics requires learners to use mathematics in ways that make them effective and involved as citizens, operate confidently and to convey their ideas and opinions clearly in a wide range of contexts (QCA, 2007: 1)

**1.2.3 A recent history of the FE sector **

By tying technical education, work-based training and adult provision together
through one single funding stream (Jarvis, 2005), the *Education Reform Act 1988 *
re-asserted the purpose of Further Education. The classical liberal roots of the ethics,
morality and the transformative opportunities brought about by education, turned to
neo-liberal and performative discourses of individualisation, economic

competitiveness, governing bodies, financial accountability and managerial control (Ball, 1990):

There shall be established a body … shall consist of fifteen members … Not less than six and not more than nine of the members shall be persons appearing to the Secretary of State … to have experience of the provision of higher education… and in appointing the remaining members to have experience of, and to have shown capacity in, industrial, commercial or financial matters or the practice of any profession (Education Reform Act, 1988: 135).

By the early 1990s the FE sector was an “industrial relations battlefield” (Shain &
Gleeson, 1999), but it was the *Further and Higher Education Act *(1992), which
irreversibly transformed provision (Coffield, 2007). In the immediate aftermath of the
Act institutions were thrust into a new marketplace where “any college could sell any
learning opportunity to anybody” (Hillier, 2006: 28).Overnight colleges became
independent corporations where the principals, suddenly in charge of multi-million
pound corporations, assumed the responsibilities of a CEO (Smith, 2007). Where the
Local Educational Authority had once overseen the organisation of provision, it
became the role of non-elected governing bodies to oversee change at a local level
(Gleeson & Shain, 1999), with the Further Education Funding Council (FEFC),
created in 1993, to implement the new funding mechanisms and to ‘claw back’ from
provisions perceived to be failing to professionalise the workforce (Hamilton &
Hillier, 2007):

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In exercising those functions a council (Further Education Funding Council) … shall have regard (so far as they think it appropriate to do so in the light of any other relevant considerations) to the desirability of maintaining what appears to them to be an appropriate balance in the support given by them as between institutions of a denominational character and other institutions (DES, 1992: 5).

The effects of the Act were profound, with key actors simply referring to working conditions as pre- or post-incorporation (Burchill, 1998). From 1997, the New Labour government reworked aspects of the post-incorporation reform agenda, but the

discursive configuration remained built around professionalism, managerial accountability, and expanding the skills-base of the adult population. In 1999, Sir Claus Moser undertook a review of literacy and numeracy provision to make recommendations which, through programmes assumed to promote integration into the labour market and more broadly into civil society, would ‘encourage’ the greatest number of ‘disadvantaged’ adults to return to the classroom. In his report, Moser estimated that about 20 per cent of the adult population, almost seven million people, “suffered” (Moser, 1999: 1) from the effects of literacy skills below those expected of an 11 year old, with the figure for numeracy as high as around 40 per cent (Moser, 1999). It was through an uneasy alliance between the twin pillars of social inclusion and economic competiveness (Schuller & Watson, 2009) that Moser constructed a policy landscape for what he termed Adult Literacy, Language and Numeracy (ALLN) provision:

Roughly 20 per cent of adults - that is perhaps as many as seven million people - have more or less severe problems with basic skills, in particular with what is generally called 'functional literacy' and 'functional Numeracy'… Poor skills are not only damaging to an individual’s chances of progression in their work, but also have an impact on performance at work with a cost to the employer. It is estimated that poor literacy and numeracy skills costs UK industry £4.8 billion each year in inefficiencies and lost orders (Moser, 1999: 20).

Moser's recommendations (detailed in Chapter five, but for the purpose of this context included new curricula, examinations and a teacher training framework) were taken up wholesale by the New Labour government and, in 2001, the Skills for Life (SfL) Strategy (DfEE, 2001) was launched. An extensive media campaign, 'Get On', reached public consciousness by highlighting the personal and national ‘cost’ of poor basic skills (Barton, 2007). The injuries caused will be discussed in more detail from Chapter five, but Raffo and Gunter (2008) comment that although the 2003 review of

23

the SfL strategy acknowledged that the ALLN targets had been surpassed, the reform agenda began to rapidly unfold through a market-led attention to human capital theory:

Inspection found that colleges and schools with sixth forms in particular had failed to respond to the requirements of the new 16 to 19 study programmes quickly enough. … English and mathematics teaching and learning are still not good enough … FE and skills providers were not adapting their provision well enough to enhance learners’ chances of future sustained employment (Ofsted, 2014: 4).

As the SfL strategy travelled through the numerous sites of delivery, Moser’s concerns
for the twin pillars of inclusion and competitiveness began to lose sight of concerns
for the effects of structural inequality (Schuller and Watson, 2009). In 2005, the Foster
Review implemented new administrative technologies to refocus delivery around one
key policy area; fostering skills in the workplace. This was immediately followed by
*The Leitch Report* (2006), which with a focus on targets reinforced the link between
LLN skills and employment and the ability for all adults to usefully participate in, and
contribute to, the prosperity of the country. The findings of the two reports were
combined by the 2006 white paper *Further Education: Raising Skills, Improving Life *
*Chances *(DfES, 2006). Wolf *et al*. (2010) deconstruct how, from this point, policy
production shifted from an understanding of ‘achievement’ based on the ability to
attain benchmarked levels of qualification, to the ‘ability’ of the institution to foster a
culture of business excellence amongst the workforce. Despite the policy claim that a
“strong focus on economic impact does not have to come at the expense of social
inclusion and equality of opportunity” (DfES, 2006: 29), by privileging skills
acquisition, policy discourse changed from the opportunities of “fostering of an
enquiring mind and the love of learning” in *TheLearning Age: A renaissance for a *
*new Britain *(DfEE, 1998) to the sector being condemned as lacking; “not achieving its
full potential as the powerhouse of a high skills economy” (DfES, 2006, foreword).
The Conservative-led coalition government, elected in May 2010, continued to reflect
Labour’s focus on ALLN, and in publishing their White Paper, *Skills for Sustainable *
*Growth,* maintained the discursive construction of the ALLN learner through emphasis
on employability, social mobility, citizenry and economic competitveness:

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Skills have the potential to transform lives by transforming life chances and driving social mobility. Having higher skills also enables people to play a fuller part in society, making it more cohesive, more environmentally friendly, more tolerant and more engaged (DBIS, 2010: 5).

Since *The Foster Report* (2005) and *The Leitch Review* (2006), policy rhetoric has lost
the structural concerns that were characteristics of Moser (1999), and with the 2011
report from DBIS (Review of Informal Adult and Community Learning) the

technologies of power have continued to shift towards a model of risk-taking ‘entrepreneurial’ education, prioritising young adults who lack English and maths skills, and those adults not in employment, and re-establish the terms ‘English’ and ‘maths’ for adults:

Our (BIS) priorities are to …Take strong action to drive up standards and quality, including withdrawing funding from providers that do not meet the high

standards that learners and employers demand and ensuring that providers support apprentices to achieve Level 2 in English and Maths (DBIS, 2011: 9).

However, the funding streams that had been established in 2001 (and sustained by the Learning Skills Council (LSC)) were split between 14-19 provision and post-19. The newly constructed Young People’s Learning Agency (YPLA) attracted most of the budget, although the Skills Funding Agency (SFA) maintained the remit for

apprenticeships. The allocation of funds for apprenticeships favoured 16-19 provision,
funding for post-19 provision was ring-fenced, although enforced through an
ever-tightening link with employability and citizenry (Hodgson, Spours & Waring, 2011).
The technologies of the funding administrations once reworked by *Further Education: *
*Raising Skills, Improving Life Chances *(DfES, 2006) as employer-led, were

transformed by *New Challenges, New Chances* (DBIS, 2011: 5) into a requirement for
colleges to collaborate with, and meet the specific demands of, local authority and
employer forums. At the time of writing, the Skills funding letter of 2015 (DBIS,
2015) reflects the responsibility of funding as shared between the employer, the sector
and, through the introduction of loans, the individual.

**1.3 The mathematical spaces created by policy discourse **

In the UK, learning mathematics is compulsory until the age of 16. For learners who achieve the threshold qualification (GCSE / level 2 mathematics), the individual is

25

then generally presented with the ‘choice’ as to whether to continue with learning mathematics. If, at age 16, the individual is unsuccessful in achieving this threshold qualification, or increasingly if they opt for a vocational pathway, they are then compelled to continue studying mathematics. At the time that I was framing the PhD research questions (October 2009), the spaces occupied by mathematics were

organised through the Skills for Life strategy (DfEE, 2001), but the sector stood
accused of failing to reorganise provision to meet the needs of employers (DfES,
2006). At the time that I collected the empirical data (December 2010 – April 2011),
*The Wolf Report *(2011) had criticised the SfL strategy, dismissing functional skills as
“conceptually incoherent” (Wolf, 2011: 172). GCSE was centre stage in the report,
which stated it was the only widely valued mathematics qualification and the
recommendation was that all adults engaged in post-16 education should repeat this
qualification, rather than engage with the alternative options such as functional skills
(Wolf, 2011).

Consequently, at the time of the field work (2011), key actors were acclimatising to
the policy shifts set out by the Conservative-led coalition. At this time, provision
remained consistent with SfL, and *New Challenges, New Chances* (DBIS, 2011)
continued the focus on the supply of employable subjects by offering Moser’s
numeracy and functional skills, with the occasional option of studying GCSE
mathematics. Since May 2015, and the installation of the Conservative government,
whilst the epistemological balance has been reworked in favour of the ‘rigorous’
content of GCSE mathematics, ‘useful’ knowledge remains constructed around
discourses of fluency, reasoning and problem solving (ETF, 2015). In addition, the
policy shift towards the delivery of ‘new’ mathematics GCSE qualifications (DBIS,
2014: 9) remains an aspiration3_{, with the majority of providers offering the functional }

skills over GCSE mathematics (ETF, 2015).

In relation to adults’ motivations to return to the classroom, it is too complex to assume homogeneity of ‘choice’. For example, according to NIACE (2011), many adult learners are compelled to return to the classroom by employers, workplace

3_{ In August 2015, raw figures from 2013 suggested that }_{110,811 learners took a GCSE mathematics exam in }

the FE sector (Porter, 2015), whereas just over one million learners took functional skills mathematics exams at this time (ETF, 2015)

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training schemes, and on the advice of professionals such as General Practitioners, etc. In this way, ‘choice’ does exist, but the conditions are inscribed through the routes by which the individual finds themselves returning to education. It is these subjectivities that are central to the findings of this thesis, and it is for this reason that I include the use of ‘choice’ but do so with extreme caution. To return to the mathematical spaces on offer at the time of the fieldwork, the most prominent space of ‘choice’ fell

between the option of studying mathematics as a discrete course (where mathematics is the only course of study), or as part of a wider vocational programme, where the mathematical element is embedded within the qualification.

On entering a mathematical programme, the level of the examination is determined by
the results of an initial assessment (Hodgson *et al*., 2011). A discrete course (where the
learning of mathematics is the only learning outcome) is usually organised around
mathematical content of the curriculum, with classes typically lasting two to three
hours. Where mathematics is delivered as part of a wider vocational learning

programme, classes tend to be about an hour in length, with the mathematical content
geared towards the relevance of the particular vocation of the student group (Hodgson
*et al*., 2011). In this instance, the level of the mathematical qualification is determined
by the wider level of the vocational course (Wolf, 2011). For example, where a learner
is studying on a level 2 vocational course, she is expected to achieve a level 2

qualification in English, and at least a level 1 qualification in mathematics. A learner on a level 1 qualification, is expected to achieve a level 1 qualification in English, and at least an upper entry level qualification in mathematics (Wolf, 2011).

At the time of the field work (December 2010 – May 2011), there were four forms on offer within the sector; adult numeracy (ALLN); functional skills mathematics; GCSE mathematics and non-accredited mathematics. It is the nuances, the (dis)continuities and tensions brought about by the experiences of learning through one curriculum, as opposed to another, that are central to the discussion threads of this thesis. For the purpose of this brief context, the teaching and learning practices of the GCSE mathematics classroom tend towards a traditional focus on learning mathematical rules and procedures (Ernest, 1998). In contrast, the alternative spaces on offer

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to emphasise the processes of 'agentic' mathematical thinking, rather than the traditional reliance on the algorithmic product.

The gap between the adult learners’ memory of classroom mathematics and the experience of mathematics in the contemporary problem-solving classroom will be detailed from Chapter six. But in terms of this context, Bernstein’s (1971, 1999) analysis of pedagogic practice can provide a theoretical understanding to support the upcoming conversations. Bernstein (1999) initially makes a distinction between vertical and horizontal discourses of knowledge. Vertical discourses consist of coherent, explicit, and systematically principled knowledge (Fitzsimons, 2002), and within this traditional pedagogic model the epistemic focus tends to centre on abstract ‘why’ principles (Coben, 2000). In contrast, horizontal discourses are comprised of segmented localised knowledge, which focus on practical questions that concern the ‘how’ of mathematical reasoning (Coben, 2000). Within this model, mathematical spaces tend to be pedagogically articulated to the adult learner, through drawing from existing funds of knowledge (Street, Baker & Tomlin, 2008). Pedagogies that bring about horizontal discourses tend to involve the affective domain, demand a repertoire of strategies from the learner, with an epistemic enquiry that tends to be directed towards individually planned for, relevant, contextualised, and time-bound goals (Fitzsimons, 2002).

Bernstein (1999) then uses the conceptual tools of classification and framing to theorise the effects of the primary technologies of power (mathematical language and codes) on the structuring processes of learning in the classroom (Fitzsimons, 2002). With its own unique identity and specialised language, mathematics is often cited as a discourse that is both strongly classified and framed. Strongly classified because there is a clear linear system for acquiring knowledge, and strongly framed because only a small proportion of the population are awarded the opportunity to progress to higher levels of mathematics and, of those, only a privileged few achieve the status of

mathematician (Walkerdine, 1998). The strong classification and framing of traditional classroom mathematics (for example GCSE) demands learners use specialised

symbolic structures (and codes), to expand their mathematical thinking. Learning is often informed by the learners’ ability and willingness to follow prescribed routes of

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enquiry. This pedagogic approach demands the teacher to be visible, situating the learner as a passive recipient of an external body of mathematical rules and procedures (Fitzsimons, 2002). The teaching, learning and assessment practices of the GCSE mathematics classroom tends towards this more traditional focus on mastering mathematical rules and prescribed procedures (Ernest, 1998).

In polar contrast, the mathematics on offer through SfL is both flexibly framed and classified (Coben, 2000). SfL mathematics is positioned as a problem-solving tool that is constructed by the individual, and which is communicable through language and symbols malleable enough to embrace everyday situations (Wolf, 2011). Within this model, learners are required to take control of their own mathematics and to make sense of their own mathematical world. Teachers become less visible and more instructional (Fitzsimons, 2002). General mathematical principles tend to become contextualised into localised settings, in ways that require the learning community to construct their own mathematics for a particular purpose (Coben, 2000). With ALLN Numeracy (DfES, 2001) and Functional Skills mathematics (QCA, 2007), SfL shifted the assessment criterion towards an inspection of the mathematical procedure, with the justification of the choice of strategy privileged over the algorithmic product.

According to authors (Baxter *et al*., 2006; Coben, 2006; Swain & Swan, 2007; Swain
*et al*., 2005) writing within the constructivist paradigm, the advantage is that learning
through horizontal discourses tends to invite intuitive meaning for the individual. The
learner is assumed to hold a greater degree of agency over the direction and purpose
of their learning. In ways similar to traditional models, learning remains organised
around building the ‘basic blocks’, in that the approach maintains the assumption that
the adult learner should be able to master adding digits before they can multiply. They
must measure with a ruler, before they can construct a graph etc. However, in a
departure from traditional pedagogic models, the adult learner is required to engage
with peer to peer co-construction of mathematical knowledge. This demands the
learner values what Usher (2002) refers to as the soft skills of the knowledge

economy; namely team work, problem solving and leadership. The consequences for learning mathematics through this perspective can be dramatic. Learners are expected to undergo transformation; to learn to value their own and their peers’ constructions of

29

mathematics; to articulate their own ideas; to explain their mathematical schemata and to take on particular subject positions, not only in relation to the forms of

mathematical knowledge, but also to the shape of delivery and as subjects of employment.

**1.4 Summary **

The intention of this opening chapter has not been to trouble the assumptions behind the ways in which adult learners are being asked to learn mathematics (such

discussions will take place from Chapter five), instead the aim has been to provide a context to frame the arguments put forward in this thesis. This study is principally concerned with interrogating narratives to reach alternative understandings of what encounters of mathematics, and indeed mathematical spaces, look and feel like from the perspective of adults returning to the classroom to learn mathematics in the FE sector. In this thesis I explore the ways in which resistance is performed, and to discuss whether it is possible to confront uncompromising discourses and continue to learn within the sector. In the next chapter, I map the existing body of knowledge (regarding the sector) and in a critical response; I look to the academic theories and discussions that have informed how I have gone about interrogating the data. I conclude with a critical analysis that puts forward the arguments for using a broadly post-structuralist approach in analysing the empirical data.

30

**Chapter 2: The literature review **

This chapter maps an existing body of knowledge, starting with an overview of the research that is specific to adults learning mathematics within the FE sector. In the second section, I map the academic debates that have informed my interrogation of the narratives of this sample of learner participants (and to an extent their teachers) to reveal how they have come to negotiate, rework and reconfigure their

(non)mathematical identities in and between the subjectivities on offer through the dominant discourses of the sector. Then in critical response, I outline my arguments for the rejection of the Humanist model of the unitary individual, and justify a move towards a broadly post-structuralist analysis of the empirical data.

**2.1 Situating this PhD within the existing body of research **

The SfL Strategy encouraged teacher participation in research, and between 2004 and 2007 the Department for Innovation, Universities and Skills (DIUS) and the National Research and Development Centre (NRDC) established a large-scale research

consortium Maths4Life (M4L), “to develop non-specialist mathematics teaching and
learning for everyday life and work” (Hudson, Colley, Griffiths & McClure, 2006: 5).
M4L commissioned 90 research projects, the most significant of which was *Thinking *
*Through Mathematics* (TTM). Although the opportunities to conduct research during
this time were extensive, the funding streams were tied to the interests of the primary
funding agents, the Department for Education and Skills (DfES) and the Department
for Innovation, Universities and Skills (DIUS). A glance through the titles of the
funded research (NRDC, 2013) during this period shows that in line with the findings
made by Coben *et al*. (2003), almost two thirds employed a design-based research
methodology, which more often than not culminated in pedagogic guides and
practitioner tool kits.

The pedagogic guides and tool kits from the research commissioned by Maths4life, and to a lesser extent the Teaching and Learning Research Programme (TLRP), fundamentally changed the landscape for teaching in the sector. The findings of TTM in particular informed the criteria that construct the common inspection framework

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(NCETM, 2008, 2011). As such, the teacher participants have, to varying degrees, attended the professional development events brought about by the findings, and whilst I intend to critically analyse the discourses of best practice, professionalism and standards, I feel it important to initially outline the influential research from which the discussions of collaborative learning and numeracy have occurred.

**2.2 Constructivist conversations of power and social justice **

In 2006, the Maths4Life consortium commissioned an extensive research project
*Thinking Through Mathematics*(TTM), which informed the Maths4Life policy

discussion paper, which in turn reworked the criterion of best practice for the common inspection framework (NCETM, 2008, 2011). On completion of TTM, the

professional development aids and learning materials were rolled out, made freely accessible to all practitioners working within the field. TTM was a design-based research project, framed by the unproblematised assumption that the individual adult learner can (and should) be taught how to construct, organise and articulate their own mathematical knowledge. The research captured data from ‘attitudinal’ surveys and from observations of classroom and CPD eventsto capture ‘typical’ teaching and learning behaviours within the classroom. Particular attention was paid to occurrences of practices “that resist change” (Swain & Swan, 2007: 7). In the findings, learner resistance was understood in terms of ‘normal’ reactions to change, and analysed in terms of persistent behavioural patterns in need of reform:

Some learners come to classes with clear expectations of the teacher, the mathematics, and the ways in which they would be expected to learn. Some found it harder, and took longer than others, to adapt to working in new ways (Swan & Swain, 2010: 170).

Although the stated desires to “challenge the status quo” (Swain & Swan, 2007: 7) and to “enhance the quality of learning” (p. 14) placed the notion of social justice at the heart of this project, TTM aimed to provide a tool kit for teaching with findings expressed in terms of clear outputs that indicated 'correct' learning procedures. In opting to express the findings in terms of a recipe for ‘best practice’, the findings demand that the ‘expert’ learner should be facilitated by the teacher, and be shown how to organise, value and articulate their own mathematical constructions. The authors were untroubled to articulate learning as a cognitive process that is

32

complicated, and disrupted, by the chaos of the affective domain. TTM, in seeking to establish an account of ‘normal’ (whether of learner behaviour, best practice or

professionalism) sustained the hegemonic illusion that there are pedagogic ‘truths’ that make learning accessible to all. As a practitioner and teacher trainer, I acknowledge that I benefited from the practical suggestions offered to me for the classroom; but simultaneously the authors, in failing to allocate the analytical spaces to interrogate the forms of resistance, sustained the status quo. Discourses of best practice, standards and professionalism have become the means by which to render a teacher or a learner ineffective because of their ‘old ways of thinking’. Simultaneously, the requirement to change is organised and monitored through new regimes of standards, which

essentialise modes of learning as effective or ineffective, often positioning the

individual as obstructive or resistant to change. I argue that it is vital to uncover some of the trajectories of the subjective ways in which individuals are required to be a ‘successful’ learner (or teacher).

The intention of this thesis is to provide a different theoretical account of resistance. By problematising the homogeneity inherent within Swain and Swan’s (2007) discursive production of concepts such as “rich collaborative tasks" (Swain & Swan, 2007: 38), “teachers’ knowledge" (p. iii), “shared goals" (p. 15) and “changes in practice" (p. 52), I turn towards discussions of the production of discourses, the representation of cultural and ideological practices, to reveal certain subjectivities and a compulsion to undergo identity work. I challenge the assumption of 'natural' truths about learning and, as such, I turn to TTM to reveal how adult learners have come to be inscribed as particular kinds of mathematical subject.

**2.3 A turn towards Lacan **

In the previous section, I illustrated how authors working within the Humanist
tradition seek to understand how an agentic individual makes sense of their
experiences of mathematics. Instead of theorising learning as primarily within the
cognitive domain, in using a Lacanian lens participation becomes “a risky business
since the threat of failure is ever present” (Black, Mendick & Solomon, 2009: 6). I
mobilise Brown (1991, 2008b), Brown *et al*. (1991, 2001, 2006), Walshaw (2004,

33

2007, 2010) and Bibby’s (2010, 2011) application of the Lacanian perspective, to ask questions of the empirical narratives to reveal psychic costs of the investment in desires, fantasies and fears, brought about by returning to the classroom to learn mathematics.

Brown (2008) utilises Žižek’s (1998, 2006) applications of Lacan’s (1977) psychoanalytical account to show how regulatory discourses silently “nudge individuals towards conventional, that is, state sanctioned modes of behaviour” (Brown, 2008c: 253). Brown tends to be critical of what he refers to as the “hardcore” (2008b: 28) constructivist approach, a location from which I situate the design-based research TTM:

I concur with those who suggest that radical constructivism provides an

inadequate account of how the social web of discourses intervenes in the process of individuals declaring how they see things (Brown, 1991: 19).

Brown and McNamara (1991, 2001) conducted two inter-related studies to explore the theoretical landscape of identity positioning within and around the discourses of mathematics. The initial study was based on a cohort of 20 trainee teachers and included participants from each phase of the four-year training cycle of a Bachelor of Education (B.Ed.) course. The second followed a smaller sample of 10 newly

qualified teachers as they transitioned from teacher training to their first year of teaching in a primary school (Brown, McNamara, Basit & Roberts, 2001). These studies collected narratives of previous and contemporary encounters of teaching and learning mathematics and included lesson observations as well as reflexive journals, to act as ‘an aide memoire’ to facilitate the interview process. Although the

methodological tools were similar to the studies conducted by Swan and Swain
(2007), on analysing the narratives Brown and McNamara asked very different
questions of the texts. They interrogated the processes of teaching and learning as a
social phenomenon, and in doing so, explored the ways in which newly qualified
teachers (NQTs) “as subjects of an emerging professionalism … navigated the opaque
and often contradictory demands of policy” (Brown *et al*., 2001: 6). The report did not
intend to provide a tool kit for ITT, but to problematise the ways in which the NQTs
were compelled to act and become “enmeshed in the performance of symbolic acts …
(as they were) inducted into school norms and classroom practices” (Brown *et al*.,

34 2001: 8).

Whilst their observations were in line with Swan and Swain’s account, these findings
were interpreted as constitutive (and constructed) to persuade Newly Qualified
Teachers (NQTs) “to opt to ‘fit in’ with school norms and practices" (Brown *et al*.,
2001: 6). In a stark contrast to TTM’s list of normal classroom behaviours, Brown *et *
*al.*’s(2006: 154) concluding comments pointed to the complexities of professional
identity, and to the tensions hidden within the hegemonic discourses of best practice,
which currently surround the teaching and learning of mathematics in the classroom:

The compliance this activated was generally seen as supporting the common good, namely the basic need for mathematics as a social project to be taught such that all pupils could engage as fully as possible … such happy resolutions … can provide effective masks to the continuing anxieties.

Walshaw (2001, 2007, 2010), like Brown, underwrites her Lacanian framework with a Foucauldian understanding of the regulatory practices that normalise how actors discuss and implement practice. Walshaw mobilises Foucault to theorise how “politics weaves itself into the very fibre of our concepts, constructs, processes and practices” (Walshaw, 2001: 484), to understand the ways in which teaching and learning are determined within, and through, the powerful and dense web of educational discourses which position learners as particular kinds of mathematical subjects. However, in ways that juxtapose Brown’s works, Walshaw reveals the effects of the binaries of logic that are at play in the classroom. Through a particular emphasis on Foucault’s latter works on the technologies of the self, she argues that despite being caught in power contestations, it is possible to talk of spaces of agency within the classroom (Walshaw, 2010). This debate will be detailed in the next chapter, but in summary Walshaw argues that the discourses of learning should be viewed as particular forms of knowledge, which produce an effect of power that then reproduces discourses through which the individual experiences their learning.

**2.4 Gendering mathematics **

Although Brown considers the gendered trajectories of discourses, he does not contemplate the particular ways in which the dominant productions, such as binary

35

gender and natural ability, discursively sustain normalised perceptions of ‘truths’
about particular ways of knowing and doing mathematics. Bibby (2010, 2011), using a
Lacanian framework, focuses on the gendered trajectories of mathematical discourses,
but her work is grounded within a Freudian perspective (as opposed to Foucauldian)
that draws from the oedipal family and the Oedipus complex to unpack individual
relationships with mathematics. Whilst I will draw from Bibby’s work to consider
Jalal, Philly and Karigalinas’ relationship with mathematics in Chapter nine, it is
Walkerdine's (1984, 1998) and Walkerdine *et al. *(2001) pivotal works that will be
central to theorising the discourses of masculinity that will be discussed from Chapters
seven through nine.

In the 1980s, Walkerdine (1984, 1986, 1988, 1989) shook what traditionally had been held as objective truth claims about the ‘problem’ of girls’ underachievement in mathematics. She revealed that this discursive construction was as much the product, as productive, of the discursive spaces available to girls within the academic discipline of mathematics. Walkerdine - by putting the narratives of girls doing mathematics, their mothers and their teachers to work - posed new questions of pedagogic

instruction. In taking this approach, she revealed how the discursive construction of ‘underperformance’ was more a case of the social construction of the subject ‘girl’, than a product of any statistical analysis of performance. Walkerdine revealed how analysis of student attainment at this time, was less about statistical analysis and more about the stories that key actors told about ‘girls’ and ‘boys’ behaviour in the

classroom.

Walkerdine moved the axis of research interrogation towards discussions of how discourse inscribes positions within the classroom, in order to unravel how classroom (and mathematical) practice leads teachers (and researchers) to (mis)recognise

discursive constructions of binary truths (such as ‘naturally gifted’ boys and ‘hard working’ girls) as natural ‘truths’ about teaching and learning. She concluded that, contrary to popularised beliefs of the period, there is in fact no identifiable period where boys outperform girls in schoolroom mathematics:

… The question then is whether girls and women are lacking or different. Most of the arguments about their performance relative to men take difference as

36

indicative as something real. High performance indicating something present, low that something is missing. The idea that girls lack spatial ability or mastery orientation or holistic thinking, or whatever the deficient model or whatever the next incapacity turns out to be, is not best served by trying to prove either that they really have it or by trying to find the cause of their deficit … such approaches tend to fall into the trap of treating these differences as caused by something real and true (Walkerdine, 1989: 29).

**2.5 Critical rejection of the unitary individual **

I use the term the ‘socio-cultural account’ to maintain a sense of the broadness of the perspectives that centre on the Humanist understanding of the rational, agentic and unitary individual. Individual learners are understood to hold a natural freedom, although autonomy within the classroom is often recognised to be productive of “historically and culturally constituted reality according to her interpretations and personal meanings” (Radford, 2008: 453). Whilst it can be acknowledged that authors working within a Humanist framework wrestle with questions of social justice,

learning tends to be theorised as a natural behaviour, with questions concerned with the socio, political and cultural locations of knowledge. Secondly, whilst spaces of uncertainty are considered, questions tend to be formed around the (un)certainty of mathematical knowledge. As Radford (2006: 54) posits:

… On one side, meaning is a subjective construct: … Meaning here is linked to the individual’s most intimate personal history and experience; it conveys that which makes the individual unique and singular. On the other side and at the same time, meaning is also a cultural construct in that, prior to the subjective experience, the intended object of the individual’s intention (l’object visé) has been endowed with cultural values and theoretical content … It is in the realm of meaning that the essential union of person and culture, and of knowing and knowledge are realized.

Within the socio-cultural account, the individual learner is framed by the conditions of
possibility that enable the self to make, and sustain, autonomous and rational choices.
Mathematics is seen as a protean body of knowledge, malleable in the hands of the
individual (Pais & Valero, 2014). Perhaps the most alluring promise is that pedagogic
truths* will* enable all individuals to overcome the injuries of their past (Brown, 2008c).
Where a ‘problem’ with learner agency is revealed, such concerns tend to be with
protecting the safety of the learning environment, often regarded as temporary,
resolvable by neatening the “clash between individual agency and social demand”